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M09.02.07 Statistical Inference
Statistical inference is central to scientific research, acting as a guide to help determine the validity of research findings. Like a referee, statistics help interpret scientific outcomes, though outcomes are always subject to error. Below is a structured outline of statistical inference steps, hypotheses, and interpretation criteria.
1. Introduction to Statistical Inference
Statistical inference in science aims to evaluate research findings by determining whether results are likely due to chance or reflect real effects. This process includes defining research questions, formulating hypotheses, and testing them using statistical criteria.
2. Steps in Statistical Inference
- Define the Research Question
- Specify what the research intends to show.
- Formulate Hypotheses
- Null Hypothesis (H₀): Suggests no effect or difference, often representing the opposite of the desired research outcome.
- Alternative Hypothesis (H₁): Implies an effect or difference exists, supporting the desired outcome.
3. Types of Hypotheses
| Hypothesis Type | Description | Example |
|---|---|---|
| One-tailed | Tests if one group is specifically greater or less than another. | Drug A is more effective than Drug B. |
| Two-tailed | Tests if two groups are different, without specifying a direction. | Drug A is different from Drug B. |
4. Hypothesis Testing and p-Values
Once data is collected, hypothesis testing begins, and results are interpreted using p-values.
- p-Value: The probability of observing the data if the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis.
- Standard Criterion: A p-value threshold (often p ≤ 0.05) determines statistical significance.
5. Interpreting p-Values
The outcome of statistical tests depends on comparing the computed p-value to a pre-established criterion, usually set at p ≤ 0.05.
| Computed p-Value | Decision | Interpretation |
|---|---|---|
| p ≤ 0.05 | Reject the null hypothesis | Statistical significance achieved; drug likely effective. |
| p > 0.05 | Fail to reject the null hypothesis | Insufficient evidence to conclude effectiveness. |
Points to Remember
- Rejecting vs. Failing to Reject: We never “accept” the null hypothesis; instead, we reject or fail to reject it.
- Errors:
- Type I Error (α): Incorrectly rejecting a true null hypothesis.
- Type II Error (β): Failing to reject a false null hypothesis.
6. Example Scenarios
| Computed p-Value | Decision | Error Risk |
|---|---|---|
| p = 0.02 | Reject the null hypothesis | Type I error risk |
| p = 0.13 | Fail to reject null hypothesis | Type II error risk |
Figures and Decision-Making Using p-Values
Figure 1. Decision-Making Based on p-Values:
- p = 0.02: Reject null hypothesis – drug works.
- p = 0.13: Fail to reject the null hypothesis – insufficient evidence that the drug works.